Type I and type II errors associated with hypothesis testing
According to Brase and Brase, the type I error occurs when the correct null hypothesis is rejected (Brase and Brase 394). The type II error, in its turn, can be attributed to the situations when the false null hypothesis is accepted (Brase and Brase 395). In other words, the specified types of errors can be generalized as false positive or false negative assumptions from the perspective of binary classification (Brase and Brase 395).
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The probability of the type I error is traditionally expressed with the help of the symbol α. The corresponding characteristics of the type II error are identified as β following the existing statistics standards (Brase and Brase 294–296). The specified types of errors are identified as new information on the subject matter is acquired and new properties of the research subject can be identified.
As far as the type I error is concerned, it is often referred to as the error of the first kind (Brase and Brase 394) and is identified as the level of significance of the test (395). It is assumed that the increase in the amount of α, which the rate and the size of the type I error are expressed with, increases both the power and the probability of the type I error (Brase and Brase 395).
The same can be said about β, which Brase and Brase (395) identify the scale and probability of making the type II error with. However, unlike the type I error, which makes one dismiss the probability of the correct null hypothesis under a specific circumstance, the type II error occurs once the false hypothesis is accepted as a plausible one (Brase and Brase 434).
When we fail to reject the null hypothesis, we do not claim that it is true. We simply claim that at the given level of significance, the data were not sufficient to reject the null hypothesis
The statement shows in a very graphic manner that making categorical claims concerning a specific phenomenon or idea in research jeopardizes the objectivity and credibility of the research outcomes. Indeed, the fact that the null hypothesis has not been subverted at a specific stage of the research does not mean that the rest of the research steps are to be terminated and that the proof for the correctness of the research hypothesis has been found.
Instead, the absence of the type I error signifies that further explorations are to be conducted so that other possible issues may be identified (Brase and Brase 394). The statement, therefore, allows for locating the key logical fallacy, which a range of inexperienced researchers are prone to making when coming across the phenomenon in question (Simon and Simon 2). The statement, thus, represents an important commentary on the nature of the type I error.
When we accept the alternate hypothesis, we do not claim that the null hypothesis is false. We do claim that at the given level of significance, the data presented enough evidence to reject the null hypothesis
Much like the statement discussed above helps locate the essence of the type I error, the specified argument allows for a better understanding of the concept of type II error. To be more specific, the statement under consideration makes it clear that the emergence of the type II error does not presuppose the cancellation of the further steps of the study and the possibility to claim the research hypothesis wrong. Instead, the statement b) explains, further analysis must be conducted so that the hypothesis could be proven wrong in a cohesive, objective, and proper manner. The type II error, therefore, should not be interpreted as the ultimate proof of the hypothesis is incorrect. Instead, the type II error shows what steps of research need to be taken further to advance the study and solve the problem required (Brase and Brase 136).
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Brase, Charles Henry, and Corrinne Pellillo Brase. “Hypothesis Testing.” Understanding Basic Statistics. 6th ed. Boston, MA: Cengage Learning, 2012. 386–441. Print.
Simon, Richard and Noah Robin Simon. “Using Randomization Tests to Preserve Type I Error with Response Adaptive and Covariate Adaptive Randomization.” Statistics and Probability Letters 81.7 (2011), 761–772. Web.